LoglikelihoodSM: Loglikelihood (semi-Markov model)

In SMM: Simulation and Estimation of Multi-State Discrete-Time Semi-Markov and Markov Models

Description

Computation of the loglikelihood starting from sequence(s), alphabet, initial distribution, transition matrix and type of sojourn times

Usage

## parametric case
LoglikelihoodSM(seq, E, mu, Ptrans, distr, param, laws = NULL, TypeSojournTime)
## non-parametric case
LoglikelihoodSM(seq, E, mu, Ptrans, distr, param = NULL, laws, TypeSojournTime)

Arguments

seq	List of sequence(s)
E	Vector of state space
mu	Vector of initial distribution of length S
Ptrans	Matrix of transition probabilities of the embedded Markov chain J=(J_m)_{m} of size SxS
distr	- "NP" for nonparametric case, laws have to be used, param is useless - Matrix of distributions of size SxS if TypeSojournTime is equal to "fij"; - Vector of distributions of size S if TypeSojournTime is equal to "fi" or "fj"; - A distribution if TypeSojournTime is equal to "f". The distributions to be used in distr must be one of "uniform", "geom", "pois", "dweibull", "nbinom".
param	- Useless if distr = "NP" - Array of distribution parameters of size SxSx2 (2 corresponds to the maximal number of distribution parameters) if TypeSojournTime is equal to "fij"; - Matrix of distribution parameters of size Sx2 if TypeSojournTime is equal to "fi" or "fj"; - Vector of distribution parameters of length 2 if TypeSojournTime is equal to "f".
laws	- Useless if distr \neq "NP" - Array of size SxSxKmax if TypeSojournTime is equal to "fij"; - Matrix of size SxKmax if TypeSojournTime is equal to "fi" or "fj"; - Vector of length Kmax if the TypeSojournTime is equal to "f". Kmax is the maximum length of the sojourn times.
TypeSojournTime	Character: "fij", "fi", "fj", "f" (for more explanations, see Details)

Details

In this package we can choose differents types of sojourn time. Four options are available for the sojourn times:

• depending on the present state and on the next state ("fij");

• depending only on the present state ("fi");

• depending only on the next state ("fj");

• depending neither on the current, nor on the next state ("f").

Value

L	Value of loglikelihood for each sequence
Kmax	The maximal observed sojourn time

Author(s)

Vlad Stefan Barbu, [e-mail]
Caroline Berard, [e-mail]
Dominique Cellier, [e-mail]
Mathilde Sautreuil, [e-mail]
Nicolas Vergne, [e-mail]

See Also

simulSM, estimMk, simulMk, estimSM

Examples

alphabet = c("a","c","g","t")
S = length(alphabet)
# creation of the transition matrix
Pij = matrix(c(0,0.2,0.3,0.5,0.4,0,0.2,0.4,0.1,0.2,0,0.7,0.8,0.1,0.1,0), 
nrow = S, ncol = S, byrow = TRUE)

Pij
#     [,1] [,2] [,3] [,4]
#[1,]  0.0  0.2  0.3  0.5
#[2,]  0.4  0.0  0.2  0.4
#[3,]  0.1  0.2  0.0  0.7
#[4,]  0.8  0.1  0.1  0.0

################################
## Parametric estimation of a trajectory (of length equal to 5000), 
## where the sojourn times depend neither on the present state nor on the next state.
################################
## Simulation of a sequence of length 5000
seq5000 = simulSM(E = alphabet, NbSeq = 1, lengthSeq = 5000, TypeSojournTime = "f", 
                init = c(1/4,1/4,1/4,1/4), Ptrans = Pij, distr = "pois", param = 2)
                
#################################
## Computation of the loglikelihood
#################################
LoglikelihoodSM(seq = seq5000, E = alphabet, mu = rep(1/4,4), Ptrans = Pij, 
distr = "pois", param = 2, TypeSojournTime = "f")

#$L
#$L[[1]]
#[1] -1475.348
#
#
#$Kmax
#[1] 10

#------------------------------#
################################
## Non-parametric simulation of several trajectories (3 trajectories of length 1000, 
## 10 000 and 2000 respectively),
## where the sojourn times depend on the present state and on the next state.
################################
## creation of a matrix corresponding to the conditional sojourn time distributions
lengthSeq3 = c(1000, 10000, 2000)
Kmax = 4 
mat1 = matrix(c(0,0.5,0.4,0.6,0.3,0,0.5,0.4,0.7,0.2,0,0.3,0.4,0.6,0.2,0), 
nrow = S, ncol = S, byrow = TRUE)
mat2 = matrix(c(0,0.2,0.3,0.1,0.2,0,0.2,0.3,0.1,0.4,0,0.3,0.2,0.1,0.3,0), 
nrow = S, ncol = S, byrow = TRUE)
mat3 = matrix(c(0,0.1,0.3,0.1,0.3,0,0.1,0.2,0.1,0.2,0,0.3,0.3,0.3,0.4,0), 
nrow = S, ncol = S, byrow = TRUE)
mat4 = matrix(c(0,0.2,0,0.2,0.2,0,0.2,0.1,0.1,0.2,0,0.1,0.1,0,0.1,0), 
nrow = S, ncol = S, byrow = TRUE)
f <- array(c(mat1,mat2,mat3,mat4), c(S,S,Kmax))
### Simulation of 3 sequences
seqNP3 = simulSM(E = alphabet, NbSeq = 3, lengthSeq = lengthSeq3, 
TypeSojournTime = "fij", init = rep(1/4,4), Ptrans = Pij, laws = f, 
File.out = NULL)

#################################
## Computation of the loglikelihood
#################################
LoglikelihoodSM(seq = seqNP3, E = alphabet, mu = rep(1/4,4), Ptrans = Pij, laws = f, 
TypeSojournTime = "fij")

#$L
#$L[[1]]
#[1] -429.35
#
#$L[[2]]
#[1] -4214.521
#
#$L[[3]]
#[1] -818.6451
#
#
#$Kmax
#[1] 4

SMM documentation built on Jan. 31, 2020, 5:07 p.m.